Law of Total Variance Decomposition

Problem

The law of total variance splits Var(X) = E[Var(X | Y)] + Var(E[X | Y]).

Given the expected conditional variance and the variance of the conditional expectation, return Var(X).

Hint

Within-group plus between-group variance.

case 1

in: [2,3]

expected: 5

case 2

in: [0,1]

expected: 1

case 3

in: [5.5,4.5]

expected: 10

Starter codePython

def law_of_total_variance_decomposition(expected_variance, variance_of_expectation):
    # Your code here
    pass

3 test cases · run your code against them in the editor